Question 1

In an experimental study, which variable is manipulated by the researcher to observe its effect on another variable?

Accepted Answer

Explanatory variable

Question 2

Which of the following best describes a scatter plot?

Accepted Answer

A graph that shows the relationship between two quantitative variables measured on the same individual

Question 3

Suppose you are analyzing the relationship between hours studied (X) and exam score (Y) for a group of students. If the linear correlation coefficient $$r is $$calculated to be $$0.85$$, what does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam score.

Question 4

Which of the following statements about the linear correlation coefficient $$r is $$TRUE?

Accepted Answer

The value of $$r is $$not resistant to outliers.

Question 5

Given the formula for the sample linear correlation coefficient:

$$ r = \frac{\sum \left( \frac{x_i - \bar{x}}{s_x} \right) \left( \frac{y_i - \bar{y}}{s_y} \right)}{n-1} $$

What does $$s_x$$ represent?

Accepted Answer

The sample standard deviation of the explanatory variable

Question 6

A scatter plot of two variables shows points that trend upward to the right. What can you conclude about the relationship between the variables?

Accepted Answer

They are positively associated.

Question 7

If the absolute value of the correlation coefficient $$|r| is $$greater than the critical value for a given sample size, what does this indicate?

Accepted Answer

A linear relation exists between the two variables.

Question 8

Which of the following is an example of a lurking variable in the context of ice cream sales and shark attacks?

Accepted Answer

The temperature or weather

Question 9

A researcher finds $$r = -0.92$$ between the number of cigarettes smoked per day and lung capacity. What does this value of $$r$$ indicate?

Accepted Answer

A strong negative linear relationship

Question 10

Which of the following best describes a situation where the points on a scatterplot do NOT show any pattern?

Accepted Answer

There is no association between the variables.

Question 11

Suppose you convert all measurements from millimeters to inches before calculating the linear correlation coefficient $$r. $$What effect does this have on the value of $$r$$?

Accepted Answer

The value of $$r$$ remains unchanged.

Question 12

Which of the following is NOT a property of the linear correlation coefficient $$r$$?

Accepted Answer

$$r is $$resistant to outliers.

Question 13

A scatter plot shows a downward trend from left to right. Which of the following statements is correct?

Accepted Answer

The variables are negatively associated.

Question 14

If a data set contains an outlier that does not follow the overall pattern, what is the likely effect on the linear correlation coefficient $$r$$?

Accepted Answer

$$r$$ may be significantly changed.

Question 15

Which of the following best describes the explanatory variable in a study examining the effect of a new medication on blood pressure?

Accepted Answer

The dosage of the new medication

Question 16

A researcher wants to test if there is a linear relationship between two variables using the correlation coefficient. What is the correct sequence of steps?

Accepted Answer

Calculate $$r$$, compare $$|r| to $$the critical value, conclude if a linear relation exists.

Question 17

Which of the following is the correct formula for the sample linear correlation coefficient $$r$$ using $$z-$$scores?

Accepted Answer

$$ r = \frac{\sum (z_{x_i} z_{y_i})}{n-1} $$

Question 18

In a study, the response variable is plotted on which axis of a scatter plot?

Accepted Answer

Vertical axis

Question 19

Which of the following scenarios best illustrates a positive association between two variables?

Accepted Answer

As the temperature increases, ice cream sales increase.

Question 20

A researcher finds $$r = 0.05$$ between two variables. What is the best interpretation?

Accepted Answer

There is little to no linear relationship.

Correlation and Scatterplots in Statistics: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드